If I were to print one on my own, what is the cheapest price point I could obtain a printer that could do enough detail to make it hard to tell the difference from the real thing.
Around 15.000 US$.
FDM printers (the most common consumer-grade ones, the ones with the roll of filament beside them) all print with distinctive layer marks. Next are resin printers, but resins tend to have a very peculiar feeling to it, that is difficult to mistake for ABS or other injection-molding plastics, when you hold them, plus they typically struggle with largish objects. So you would probably be looking at a sintering printer, melting nylon powder with a laser. That is expensive to buy and very expensive to operate.
Now, while the above is all technically true, it is only half the story...
In fact prints done on a cheap FDM printer can be post-processed to look almost indistinguishable from an injection molded model. That takes probably more work to accomplish than modelling the object in cad and printing it though, so it's a matter of setting your expectations correctly (don't think to your print as "the product" but as the "base material" for your finished product).
I would say that you essentially have two options:
- if you are looking at picking up a new hobby, and do a lot of sanding and polishing in the process, then: "welcome to the club!". There are plenty of relatively cheap printers that can print acceptably well (more on this below).
- if your interest is not towards 3d printing in general but is really limited to getting project done, than you could consider having a printing service doing that for you instead (basically you send them the file with your design and choose what kind of printer and material you want them to use, and they send you back the end result). It will be cheaper and probably of a higher quality than what you could achieve yourself. Certainly it will require less time investment from your side.
If you go with option one, an affordable printer that got very good reviews from trustworthy reviewers is the cetus. It is 299 US$, have quality components and is very very silent. The build volume is not huge but should be more than enough for your project.
However don't take my suggestion as "this is the best you can buy for your money": there are plenty of models out there that will get the job done in the price range 300-500 US$, and if you are wishing to spend a bit more, you could get an Original Prusa MKIIs (the printer that topped the charts last year) for 600US$ as a kit or slightly more fully assembled.
Should you go for using a printing service instead, there are a lot of them. Two among the most well known are 3dhubs and shapeways.